tldr: Moving from one drive to another drive can be faster, especially with rotational storage!
What really matters isn't if the move is staying within the same drive. What matters is if the move is staying within the same filesystem.
This is more correct than referring to partitions as do some comments. (Take for example an lvm partition with two LVs in it. Same penalty moving between them as would be between two partitions.)
This pedantry is rather important: Drive, Partition, Filesystem, are not interchangeable despite most people taking that for granted.
There is no spoon:
Moves aren't what you think they are, inside a filesystem. In fact, the notion of physical location, inside a filesystem, is false. The whole hierarchical structure is much a facade put on to help us humans visualize things. You should think of all files within a filesystem as randomly numbered objects in a database table. One of the fields in that table is the random number, another is the data itself, another permissions, and one is the full file path.
Moving a file then is just as simple as updating the tiny field that says the path to that file. And that's what it is in most filesystems.
"Compressed Dirs" and "Encrypted Dirs" add more I/O to a move. As could BTRFS subvolumes, and some other trick features. But generally this is how a move works in most filesystems.
Once you move a file from one filesystem to another filesystem however, the entirety of that file's contents have to be read and written to disk. And if you have two disks to share that IO load it will be much faster. Especially considering all the head movement in a rotational drive.